First, I've seen just as many lost weight belts as lost weight pockets. So I don't think that is a strong argument for belts.
I used a weight belt exclusively for the first couple of years. Once I tried weight integrated I found I liked it better. I recently tried a borrowed BC with weight belt to see how I liked I and I still like weight integrated best.
If you go weight integrated, I recommend that weight pockets secure with both mechanical and velcro.
Try before you buy.
The reason you see people lose weight belts is because they are using the wrong ones. The reason you see so many people using integrated weights is because their alternative has been the WRONG weight belt.
I can't tell you how many people select a soft weightbelt with lead shot bags that slips and slides around their waist and before the dive is half over, the buckle is located behind them and hidden under the tank. This is a dangerous. They have no access to the buckle to tighten it or to ditch it.
People using normal nylon belts in cold water have a huge problem with suit compression on descent. With integrated weights they don't have to really worry about this.. the BC may get a little sloppy, but it will not fall off them like a weightbelt that has become too loose will. So to these people, the integrated weights have solved the problem.. but the solution is far from optimum in my opinion.
They often compound their problems by using crappy plastic buckles.
The solution to all this nonsense is the use of an elastic rubber belt. They automatically compensate for suit compression (no need to adjust) and the rubber of the belt tends to be tacky, so it does not slide around at all. Basically ALL freedivers know this already, but for some reason, they have not been adopted by the scuba industry. The buckles are also NOt prone to popping open and they do ditch extremely rapidly when opened. In fact, due to the elasticity of the belt and the unique construction and attachment of the buckle, the belt will activelyy "spring" open when the release is triggered. If anybody has to get rid of lead in a hurry, it is a freediver!
As the diving public gets older (and rounder) there is, in many cases, no longer a waist to even hold a nylon belt. There is no wonder people prefer the weights in the BC if the only option they are aware of is a belt that will slide off, spin around, require adjustment during the dive ....or require the thing to be so damn tight on the surface that the buckle is ready to break and they can't breathe properly.
If a diver is using little or no exposure protection, these problems are obviously less acute.
A rubber belt solves many problems and it can be worn in a variety of positions, that will make it more comfortable..for example, it can be worn low on the butt, across the butt or higher across the lower back. What we want to avoid is having a belt very tight across the lower abdomen because this inhibits "belly breathing" which is essential for effective and relaxed respiration. Freedivers know all this..
Why can't scuba divers figure this stuff out?
I personally prefer having a weightbelt because I can use it before scuba diving during freediving with a wetsuit. Integrated weights, kill my back when I change the BC from one tank to another and make the tank itself harder to manage. Use of weight integrated BC in coldwater also presents some complications if you remove the BC/scuba unit to address an entanglement issue... The diver will be buoyant and the scuba unit will be very negative... an unnessary hindrance during a potentially stressful situation. I won't say it is unsafe, but it is NOT desirable.
I have no problems with some weights being integrated, but I much prefer a rubber weightbelt.